Basics about pairs trading (stat arb)??

Hello friends, this is my first post here. Been lurking a while, but now I have question as I get more and more interested, I hope someone can help me, would be much appreciated!

fact A) When I trade a pair, I choose to use dollar neutral strategy. That is, I spend equal amount of money on short and long side in the pair. This means I buy X amount of stock1, and short Y amount of stock2, where X != Y.

fact B) I have also identified some cointegrated pairs. When I calculate the adf test I also get a hedge ratio, so I can form the spread which is likely to be mean reverting:
Spread = s1 - hedgeratio * s2
This means I should buy One s1 stock, and short hedgeratio*s2 stock.

My question is, how are X and Y and One and hedgeratio related to each other?

Apparently, I should short Y amount of s2 stock because A) says so. But B) says I should short hedgeratio amount of s2 stock. So, could this be the answer, maybe?:

Another question, I look for a trade signal, typically it is s1/s2 and then I check the std dev. But I trade the Spread.
So the trade signal has a weight of one s1 divided by one s2. But I trade this: buy one s1 and sell hedgeratio*s2. This means my trade signal will be on something, but I will trade on something else!!! That is weird? Can I really do like this?

The trade signal should be modified to s1/(hedgeratio*s2) or? Can anyone shed some light on this? Would be much appreciated!

I will tak a shot here to comment on the second question. Plotting the ratio in Excel
Of Oil/notes, for example only, would be dominated by the volatility of oil and the graph would look very similar to oil. Placing 2std bands around this chart and buying the ratio (oil/notes)
or selling the ratio(notes/oil) based on tags or xovers of the bands may not be what you want and not all that different from oil. Maybe try this.
First, 3x (approx) the ATR or daly % change of notes and then do the ratio of oil/3xnotes to plot with bands. You will now have entirely different entry and exit signals in your testing(tags and xovers etc..). It is dollar neutral now too if I'm not mistaken.
Show me a package that does this easily on lots of spreads and that would be nice.
By the way, see "Bone" posts here as he seems the resident expert. Good luck.